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Consider the following game. -2,-1 -2,2 8,8 Let a be the probability that P1 plays A...
Consider the following extensive form game P1 RP:2 L2 R2 L1 R1 (2,2) (0,3) 1. How many sub-games are there in this game...
Consider the following extensive form game P1 RP:2 L2 R2 L1 R1 (2,2) (0,3) 1. How many sub-games are there in this game? What is the Subgame Perfect Equilibrium? 2. Represent this game as a Normal form game and find all pure strategy Nash Eq. Is there a mixed Nash eq. in this game? If yes, show one. If not, argue why not 3. Now assume that P2 cannot observe P1's action before he makes his move. As such, he...
3. Consider the following two-player game in strategic form LM R A 2,2 2,2 2,2 В 3,3 0,2 0,0 С 0,...
3. Consider the following two-player game in strategic form LM R A 2,2 2,2 2,2 В 3,3 0,2 0,0 С 0,0 3,2 0,3 This game will demonstrate several methods for ruling out possible mixed- strategy equilibria (a) What are the pure strategy equilibria? (b) Show that there does not exist an equilibrium in which Player 1 (the row player) assigns strictly positive probability to A, to B, and to C. (c) Show that there does not exist an equilibrium in...
1. P1 and P2 play the game shown below. P1 believes that P2 will play Left with probability and Right with probability...
1. P1 and P2 play the game shown below. P1 believes that P2 will play Left with probability and Right with probability 2. Find the expected payoff for P1 if P1 plays Top and Bottom with equal probability. (2 points) Player 2 Left Right Player 1 Тор 4, 1 0,0 Bottom 2, 5 1,0 2. Find all the strategy profiles that are Pareto efficient for the game shown below.(2 points) Player 2 Left Middle Right 1,0 Player 1 Up 4,...
Consider the following extensive-form game with two players, 1 and 2. a). Find the pure-strategy Nash...
Consider the following extensive-form game with two players, 1
and 2.
a). Find the pure-strategy Nash equilibria of the game. [8
Marks]
b). Find the pure-strategy subgame-perfect equilibria of the
game. [6 Marks]
c). Derive the mixed strategy Nash equilibrium of the subgame.
If players play this mixed Nash equilibrium in the subgame, would 1
player In or Out at the initial mode? [6 Marks]
[Hint: Write down the normal-form of the subgame and derive the
mixed Nash equilibrium of...
2. (15 points) Consider the following 2 x 2 game: T B L R 3, 75....
2. (15 points) Consider the following 2 x 2 game: T B L R 3, 75. 2 6, 31, 10 Let p be the probability that player 2 plays R and let q be the probability that player 1 plays T. Draw a pair of axes with p on the horizontal axis and q on the vertical axis. Draw two lines, one indicating player 1's best response(s) as a function of p and another indicating player 2's best response(s) as...
Which one of the following description is wrong?* 1 point x 8,8 ca Y X >0,0...
Which one of the following description is wrong?* 1 point x 8,8 ca Y X >0,0 2,2 B Y 6,6 5, 5 O There are 2 pure-strategy Nash Equilibria. There exists some strictly dominated strategy. O There are infinite mixed-strategy Nash Equilibria. 0 (0,0,1),(1/4, 3/4)) is a mixed-strategy Nash Equilibrium.
Please answer 3 Questions, thank you. 4. Consider the following game: PLAYER 2 (0,3) (2,0) (1,7)...
Please answer 3 Questions, thank you.
4. Consider the following game: PLAYER 2 (0,3) (2,0) (1,7) PLAYER 1 (2,4) (0,6) (2,0) (1,3) (2,4) (0,3) a) Does this game have any pure-strategy Nash equilibrium? If so, identify it (or them) and explain why this is an equilibrium. b) Find a mixed-strategy Nash equilibrium to this game and explain your calculations. Note: a mixed strategy for player i may be expressed by o; = (P1, P2, 1- P1 - p2). c) Is...
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2....
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2. After having observed the choice of A, Player B chooses between two projects P1 or P2. The payoffs are as follows: If A chooses TI and B chooses Pl the payoffs are (12.8), where the first payoff is for A and the second for B; if A chooses TI and B opts for P2 the payoffs are (20,7); if A chooses T2 and B...
player 2 H T player 1 H 1,-1 -1,1 T -1,1 1,-1 Consider a game of...
player 2 H T player 1 H 1,-1 -1,1 T -1,1 1,-1 Consider a game of matching pennies as described above. If the pennies match player 2 pays player 1 $1 (both get head or tail). If the pennies are not matched player 1 pays player 2 $1 ( head , tail or tail , head). H represents heads and T represents Tails 1. (2 points) What is the set of strategies for each player? 2. (5 points) Is there...
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2....
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2. After having observed the choice of A, Player B chooses between two projects Pl or P2. The payoffs are as follows: If A chooses TI and B chooses P1 the payoffs are (12, 8), where the first payoff is for A and the second for B; if A chooses T1 and B opts for P2 the payoffs are (20, 7); if A chooses T2...
Consider the following extensive form game P1 RP:2 L2 R2 L1 R1 (2,2) (0,3) 1. How many sub-games are there in this game? What is the Subgame Perfect Equilibrium? 2. Represent this game as a Normal form game and find all pure strategy Nash Eq. Is there a mixed Nash eq. in this game? If yes, show one. If not, argue why not 3. Now assume that P2 cannot observe P1's action before he makes his move. As such, he...
3. Consider the following two-player game in strategic form LM R A 2,2 2,2 2,2 В 3,3 0,2 0,0 С 0,0 3,2 0,3 This game will demonstrate several methods for ruling out possible mixed- strategy equilibria (a) What are the pure strategy equilibria? (b) Show that there does not exist an equilibrium in which Player 1 (the row player) assigns strictly positive probability to A, to B, and to C. (c) Show that there does not exist an equilibrium in...
1. P1 and P2 play the game shown below. P1 believes that P2 will play Left with probability and Right with probability 2. Find the expected payoff for P1 if P1 plays Top and Bottom with equal probability. (2 points) Player 2 Left Right Player 1 Тор 4, 1 0,0 Bottom 2, 5 1,0 2. Find all the strategy profiles that are Pareto efficient for the game shown below.(2 points) Player 2 Left Middle Right 1,0 Player 1 Up 4,...
Consider the following extensive-form game with two players, 1
and 2.
a). Find the pure-strategy Nash equilibria of the game. [8
Marks]
b). Find the pure-strategy subgame-perfect equilibria of the
game. [6 Marks]
c). Derive the mixed strategy Nash equilibrium of the subgame.
If players play this mixed Nash equilibrium in the subgame, would 1
player In or Out at the initial mode? [6 Marks]
[Hint: Write down the normal-form of the subgame and derive the
mixed Nash equilibrium of...
2. (15 points) Consider the following 2 x 2 game: T B L R 3, 75. 2 6, 31, 10 Let p be the probability that player 2 plays R and let q be the probability that player 1 plays T. Draw a pair of axes with p on the horizontal axis and q on the vertical axis. Draw two lines, one indicating player 1's best response(s) as a function of p and another indicating player 2's best response(s) as...
Which one of the following description is wrong?* 1 point x 8,8 ca Y X >0,0 2,2 B Y 6,6 5, 5 O There are 2 pure-strategy Nash Equilibria. There exists some strictly dominated strategy. O There are infinite mixed-strategy Nash Equilibria. 0 (0,0,1),(1/4, 3/4)) is a mixed-strategy Nash Equilibrium.
Please answer 3 Questions, thank you.
4. Consider the following game: PLAYER 2 (0,3) (2,0) (1,7) PLAYER 1 (2,4) (0,6) (2,0) (1,3) (2,4) (0,3) a) Does this game have any pure-strategy Nash equilibrium? If so, identify it (or them) and explain why this is an equilibrium. b) Find a mixed-strategy Nash equilibrium to this game and explain your calculations. Note: a mixed strategy for player i may be expressed by o; = (P1, P2, 1- P1 - p2). c) Is...
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2. After having observed the choice of A, Player B chooses between two projects P1 or P2. The payoffs are as follows: If A chooses TI and B chooses Pl the payoffs are (12.8), where the first payoff is for A and the second for B; if A chooses TI and B opts for P2 the payoffs are (20,7); if A chooses T2 and B...
player 2 H T player 1 H 1,-1 -1,1 T -1,1 1,-1 Consider a game of matching pennies as described above. If the pennies match player 2 pays player 1 $1 (both get head or tail). If the pennies are not matched player 1 pays player 2 $1 ( head , tail or tail , head). H represents heads and T represents Tails 1. (2 points) What is the set of strategies for each player? 2. (5 points) Is there...
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2. After having observed the choice of A, Player B chooses between two projects Pl or P2. The payoffs are as follows: If A chooses TI and B chooses P1 the payoffs are (12, 8), where the first payoff is for A and the second for B; if A chooses T1 and B opts for P2 the payoffs are (20, 7); if A chooses T2...
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